On Radical Concept in Sheffer Stroke Basic Algebras
Project no. 32033 · Status: Kapanmış (Yayın bekleniyor) · 2023
Summary
<p>In this project, a detailed examination of radicals of ideals in Sheffer stroke elementary algebras is aimed. In this context, the concept of radical of ideals will be defined with the elements of Sheffer stroke elementary algebraic structure and its relations with radical ideals in MV-algebras will be examined. At the same time, the concept of semi-maximal ideal in Sheffer stroke elementary algebras will be introduced and the relations of this concept with other multi-valued algebras will be determined. Regarding the mentioned structures, necessary and sufficient conditions for semi-maximal ideals to be possible in Sheffer stroke elementary algebras will be investigated and the properties of radical ideals in these algebras will be determined in detail. In the next step of the research, the characterization of radical ideals, their relations in different algebras, common aspects and differences of semi-maximal ideals and filters will be tried to be revealed. In addition, it is aimed to determine the common aspects and relations of ideals and semi-maximal ideals in different algebraic structures with Sheffer stroke restriction and to clarify them in Sheffer stroke elementary algebra. It is aimed to support each of these steps examined during the project with non-obvious examples. As a result, when this study is completed, the important structural properties of ideals and semi-maximal ideals on Sheffer stroke elementary algebras will be explained in detail, and with the help of these, the concept of radical on Sheffer stroke elementary algebras will be defined for the first time.</p>